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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (10): 2116-2125    DOI: 10.3785/j.issn.1008-973X.2023.10.020
    
Identification method of cross-scale mesh and application in analysis of cutoff wall
Xiang YU1,2(),Yuan-ping LAI2,Yu-ke WANG2,*(),Yong-qian QU3,Hao-ran ZHENG2
1. Key Laboratory of Engineering Geophysical Prospecting and Detection of Chinese Geophysical Society, Wuhan 430000, China
2. School of Water Conservancy and Civil Engineering, Zhengzhou University, Zhengzhou 450001, China
3. School of Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China
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Abstract  

A cross-scale mesh identification method was presented to efficiently create two-dimensional scaled boundary finite element method-finite element method (SBFEM-FEM) cross-scale coupled meshes. The method combined the artificially controllable characteristics of CAD to identify, cut, and organize graphic line segments generating effective nodes and line segments. A reasonable polygonal-scaled boundary element or finite element was generated based on the topological relationship between the nodes and the line segments and the construction of the closed domain. The nodes and element information were assembled. The two-dimensional SBFEM-FEM cross-scale coupled mesh suitable for numerical analysis was produced. The stress and deformation distribution law and peak value of the wall obtained by different mesh generating methods were compared and studied to verify the validity and calculation accuracy of the generated SBFEM-FEM cross-scale coupling mesh based on a dam project. Results showed that the error of the principal stress obtained by the conventional large-scale finite element mesh simulation could exceed 48%, the error of the results obtained based on the proposed cross-scale fine numerical mesh could not exceed 5%, and the number of mesh elements was greatly reduced. The cross-scale mesh identification method can provide strong support for the anti-seepage structures in dam engineering.

Key words： coupled scaled boundary finite element method-finite element method      generation of cross-scale mesh      refined simulation      cutoff wall of embankment      controllability     
Received: 30 November 2022      Published: 18 October 2023
CLC:  TV 39  
Fund:  中国地球物理学会工程物探检测重点实验室开放研究基金资助项目（CJ2021D05）；国家自然科学基金资助项目（52192670, 52109151, 51809034）；中国博士后科学基金资助项目（2021M692938）；河南省省重点研发与推广专项资助项目（222102320098）；云南省重大科技专项计划资助项目（202102AF08002）
Corresponding Authors: Yu-ke WANG     E-mail: xiangyu@zzu.edu.cn;ykewang@163.com
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Xiang YU
Yuan-ping LAI
Yu-ke WANG
Yong-qian QU
Hao-ran ZHENG
Cite this article:

Xiang YU,Yuan-ping LAI,Yu-ke WANG,Yong-qian QU,Hao-ran ZHENG. Identification method of cross-scale mesh and application in analysis of cutoff wall. Journal of ZheJiang University (Engineering Science), 2023, 57(10): 2116-2125.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.10.020     OR     https://www.zjujournals.com/eng/Y2023/V57/I10/2116


跨尺度网格识别方法及在防渗墙分析中的应用

为了高效地生成二维比例边界有限元-有限元（SBFEM-FEM）跨尺度耦合网格，提出跨尺度网格识别方法. 该方法结合CAD人为可控的特点，对图形线段进行识别、裁剪、整理，生成有效节点与线段；根据节点与线段的拓扑关系以及封闭域的构造，生成合理的多边形比例边界单元或有限单元；最后组装节点与单元信息，输出可以用于数值分析的二维SBFEM-FEM跨尺度耦合网格. 为了验证生成SBFEM-FEM跨尺度耦合网格的有效性及计算精度，依托某堤坝工程，对比分析了防渗墙不同网格剖分方法获得的墙体应力变形分布规律及峰值. 结果表明，采用常规大尺度有限元网格模拟获得的主应力误差可以超过48%，基于所提跨尺度精细数值网格获得的结果误差不能超过5%，且其网格单元量大幅度降低. 跨尺度网格识别方法可以为堤坝工程防渗结构提供有力的支持.


关键词： SBFEM-FEM耦合,  跨尺度网格生成,  精细模拟,  堤坝防渗墙,  可控性 
Fig.1 Boundary discrete element in scaled boundary finite element method
Fig.2 Schematic diagram of cross-scale mesh transition method
Fig.3 Schematic diagram of cantilever beam structure
Fig.4 Simplified schematic diagram of cantilever beam structure
Fig.5 Basic mesh diagram of cantilever beam structure
节点编号 1 2 3 4 5 6 7 8
1 — 1 — — — 1 — —
2 1 — 1 1 — — — —
3 — 1 — — 1 — — —
4 — 1 — — 1 — 1 —
5 — — 1 1 — — — 1
6 1 — — — — — 1 —
7 — — — 1 — 1 — 1
8 — — — — 1 — 1 —
Tab.1 Node connection relation matrix A
Fig.6 Relationship diagram of node connection
节点编号 1 2 3 4 5 6 7 8
连接数目 2 2 1 2 1 1 1 0
Tab.2 Number of node connections vector
Fig.7 Identification method and process of unit generation
Fig.8 Cross-scale mesh of cantilever beam structure of final identification
Fig.9 Sketch of material distribution and load steps of embankment
Fig.10 Schematic diagram of force on anti-seepage system
材料 $ {\gamma _{\text{d}}} $/(kg·m?3) $ {\gamma _{\text{f}}} $/(kg·m?3) $ k $ $ {k_{{\text{ur}}}} $ $ \;\beta $ $ {n_{{\text{ur}}}} $
坝体 16.3 982 300 360 0.34 0.34
坝基 16.5 982 320 390 0.30 0.30
材料 $ {R_{\text{f}}} $ $ {k_{\text{b}}} $ $ q $ $ c $/kPa $ \varphi $/(°) $ \Delta \varphi $/(°)
坝体 0.95 200 0.30 22.2 11.3 0
坝基 0.95 215 0.30 21.6 11.8 0
Tab.3 Static parameters of dam body and foundation
材料 $\; \rho$/(kg·m?3) $ E/{\text{MPa}} $ $ \nu $
混凝土防渗墙 2 400 30 000 0.167
基岩 2 400 200 0.350
Tab.4 Static parameters of wall and bedrock
位置 $ K $ $ j $ $ \delta /(^\circ ) $ $ {R_{\text{f}}} $ $ c/{\text{kPa}} $
墙与坝体 757 0.8 11.0 0.89 10.5
墙与坝基 757 0.8 11.0 0.89 10.5
Tab.5 Static parameters of contact surface
Fig.11 Diagram of local elements of wall and soil
Fig.12 Coupling SBFEM-FEM mesh after mesh recognition
M N* N n* H1/m H2/m
1 14 906 14 560 144 0.500 0.125
2 15 381 14 968 552 0.125 0.125
3 48 075 47 634 552 0.125 0.125
Tab.6 Information of node and unit
Fig.13 Element number of dam and wall for three conditions
Fig.14 Distribution of dam displacement after impoundment
Fig.15 Horizontal displacement of wall after impoundment
Fig.16 Maximum and minimum principal stress distribution of wall in upstream after impoundment
Fig.17 Maximum and minimum principal stress distribution of wall in downstream after impoundment
Fig.18 Maximum and minimum principal stress distribution of embankment in downstream after impoundment
模型 上游 $ {\sigma _1} $ 上游 $ {\sigma _3} $ 下游 $ {\sigma _1} $ 下游 $ {\sigma _3} $
F/MPa D/% F/MPa D/% F/MPa D/% F/MPa D/%
1 3.76 19.7 ?0.16 48.80 0.26 29.50 ?3.37 20.88
2 4.63 1.11 ?0.29 4.43 0.36 3.74 ?4.20 1.43
3 4.69 — ?3.04 — 0.38 — ?4.26 —
Tab.7 Principal stress of wall for three conditions
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